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**Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts**

Question 1.

Express each of the following statements in algebraic form :

(i) The sum of 8 and x is equal to y.

(ii) x decreased by 5 is equal to y.

(iii) The sum of 2 and x is greater than y.

(iv) The sum of x and y is less than 24.

(v) 15 multiplied by m gives 3n.

(vi) Product of 8 and y is equal to 3x.

(vii) 30 divided by b is equal to p.

(viii) z decreased by 3x is equal to y.

(ix) 12 times of x is equal to 5z.

(x) 12 times of x is greater than 5z.

(xi) 12 times of x is less than 5z.

(xii) 3z subtracted from 45 is equal to y.

(xiii) 8x divided by y is equal to 2z.

(xiv) 7y subtracted from 5x gives 8z.

(xv) 7y decreased by 5x gives 8z.

Solution:

Question 2.

For each of the following algebraic expressions, write a suitable statement in words:

(i) 3x + 8=15

(ii) 7 – y > x

(iii) 2y – x < 12

(iv) 5 ÷ z = 5

(v) a + 2b > 18

(vi) 2x – 3y= 16

(vii) 3a – 4b > 14

(viii) b + 7a < 21

(ix) (16 + 2a) – x > 25

(x) (3x + 12) – y < 3a

Solution:

Question 1.

Separate the constants and the variables from each of the following:

Solution:

Question 2.

Group the like terms together :

Solution:

Question 3.

State whether true or false :

(i) 16 is a constant and y is a variable but 16y is variable.

(ii) 5x has two terms 5 and x.

(iii) The expression 5 + x has two terms 5 and x

(iv) The expression 2x^{2} + x is a trinomial.

(v) ax^{2} + bx + c is a trinomial.

(vi) 8 x ab is a binomial.

(vii) 8 + ab is a binomial.

(viii) x^{3} – 5xy + 6x + 7 is a polynomial.

(ix) x^{3} – 5xy + 6x + 7 is a multinomial.

(x) The coefficient of x in 5x is 5x.

(xi) The coefficient of ab in – ab is – 1.

(xii) The coefficient of y in – 3xy is – 3

Solution:

Question 4.

State the number of terms in each of the following expressions :

Solution:

Question 5.

State whether true or false:

(i) xy and – yx are like terms.

(ii) x^{2}y and – y^{2}x are like terms.

(iii) a and – a are like terms.

(iv) – ba and 2ab are unlike terms.

(v) 5 and 5x are like terms.

(vi) 3xy and 4xyz are unlike terms.

Solution:

Question 6.

For each expression, given below, state whether it is a monomial, or a binomial or a trinomial.

Solution:

Question 7.

Write down the coefficient of x in the following monomial :

Solution:

Question 8.

Write the coefficient of :

Solution:

Question 9.

State the numeral coefficient of the following monomials :

(vii) – 7x ÷ y

(viii) – 3x ÷ (2y)

Solution:

Question 10.

Write the degree of each of the following polynomials :

Solution:

Question 1.

Express each of the following statements in algebraic form :

(i) The sum of 3x and 4y is 8.

(ii) 5x decreased by 7 gives y.

(iii) 31 added to 4x gives 6x.

(iv) 3x subtracted from 89 gives 44.

Solution:

Question 2.

Group the like terms :

Solution:

Question 3.

Write the number of terms in each of the following polynomials :

Solution:

Question 4.

For each expression, given below, state whether it is a monomial, or a binomial or a trinomial:

(i) x + y

(ii) 5x – 4y

(iii) 7x^{2} + 5x + 8

(iv) 64 + 3 ÷ 6

(v) 9 ÷ a x b

(vi) 8a ÷ b

Solution:

Question 5.

Write the coefficient of x2y in :

(i) -7x^{2}yz

(ii) 8abx^{2}y

(iii) – x^{2}y

Solution:

Question 6.

Write the coefficient of :

(i) x^{2} in – 8x^{2}y

(ii) y in -4y

(iii) x in – xy^{2}

Solution:

Question 7.

Write the numeral coefficient in :

Solution:

Question 8.

Write the degree of each of the following polynomials :

Solution:

Question 9.

Write each statement, given below in algebraic form :

(i) 28 more than twice of x is equal to 45.

(ii) 3y reduced by 5z is greater than 8x.

(iii) 6x divided by 13y is less than 17.

(iv) 9 multiplied by 5x is equal to 2y.

Solution:

Question 10.

State whether true or false :

(i) If 23 is a constant and x is a variable, 23 + x is constant.

(ii) If 23 is a constant and x is a variable, 23x is a variable.

(iii) If y is a variable and 57 is a constant, y – 57 is a variable.

(iv) If 3x and 2y are variable; each of 3x + 2y, 3x – 2y, 3x ÷ 2y and 3x x 2y is a variable.

Solution:

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